Many Connecticut genealogy records can be found in old books linked on the Connecticut Resources page, where you can find resources by counties and towns, but if you're still having trouble finding the records you seek, they may have been lost or destroyed.
Following is a list of records of Connecticut's Congregational Churches known to have been lost or destroyed:
Andover - The Congregational Church of Andover, est. 1749: Births & marriages before 1818 burned.
Bethany - The Congregational Church of Bethany, est. 1763: Before 1823, lost.
Bristol - The Congregational Church of Bristol, est. 1747: No marriages before 1792; baptisms begin 1800.
Canterbury (Westminster) - Records from the Congregational Church in Canterbury from its organization in 1770 to 1824 were lost. Records from Canterbury's First Congregational Church from 1712-1771 are available, however.
Canton Center - The Congregational Church of Canton Center, est. 1750: Before 1826, lost.
Coventry - The 2nd Congregational Church of Coventry, est. 1745: None before 1818.
East Granby - The Congregational Church of East Granby, est. 1737: Lost?
East Haddam (Hadlyme) - The Congregational Church of East Haddam (Hadlyme), est. 1745: No marriages before 1800; baptisms begin 1745.
Eastford - The Congregational Church of Eastford, est. 1778: No records before 1800.
Ellington - The Congregational Church of Ellington, est. 1736: Lost.
Goshen - The Congregational Church of Goshen, est. 1740: Lost.
Greenwich - The 1st Congregational Church of Greenwich, est. 1670: Nothing before 1787.
Greenwich (Stanwich) - The Congregational Church of Greenwich (Stanwich), est. 1735: Burned 1821.
Harwinton - The Congregational Church of Harwinton, est. 1738: Nothing before 1790.
Hebron - The 1st Congregational Church of Hebron, est. 1717: Records burned.
Litchfield - The Congregational Church of Litchfield, est. 1721: Before 1886, burned.
Lyme - The 2nd Congregational Church of Lyme, est. 1719: Lost.
Lyme - The 3rd Congregational Church of Lyme, est. 1727: Lost.
Marlborough - The Congregational Church of Marlborough, est. 1749: Missing.
Middlefield - The Congregational Church of Middlefield, est. 1745: No records before 1808.
Middletown (South) - The 2nd Congregational Church of Middletown (South), est. 1747: No records before 1800.
Monroe - The Congregational Church of Monroe, est. 1764: No marriages before 1821; baptisms begin 1776.
North Guilford - The Congregational Church of North Guilford, est. 1725: Lost.
Plymouth - The Congregational Church of Plymouth, est. 1740: No marriages before 1800.
Ridgefield - The 1st Congregational Church of Ridgefield, est. 1714: Nothing before 1800.
Salisbury - The Congregational Church of Salisbury, est. 1744: No records before 1800.
Sherman - The Congregational Church of Sherman, est. 1744: Burned.
South Manchester - The Congregational Church of South Manchester, est. 1779: Lost?
Suffield (West) - The Congregational Church of Suffield (West), est. 1744: No records before 1840.
Tolland - The Congregational Church of Tolland, est. 1723: Records burned.
Torringford - The Congregational Church of Torringford, est. 1764: Records before 1837 burned.
Watertown - The Congregational Church of Watertown, est. 1739: Records lost.
West Haven - The Congregational Church of West Haven, est. 1719: Records before 1815, lost.
Source: Early Connecticut marriages as found on ancient church records prior to 1800, by Bailey, Frederic William, 1896.